The brain is an extremely complex network consisting of billions of neurons linked by trillions of synapses. Neuronal function depends on how these neurons are connected within this network. A wide range of brain functions, including sensory perception, learning, memory, decision making, cognition, reasoning, and communication, is therefore related to the details of this neuronal connectivity. Many neuropsychiatric and neurodegenerative disorders, including schizophrenia, autism spectrum disorders, Alzheimer's and Parkinson's diseases, are linked to abnormal changes in neuronal connectivity. Understanding neuronal circuitry is therefore a task of enormous importance. Despite the progress made by using microscopic and electrophysiological approaches, especially for small networks, understanding neuronal connectivity has been stalled by astronomical complexity of this task. Here we propose to provide the computational and theoretical foundations for a novel technology which will dramatically accelerate our capacity to determine neuronal connectivity with single-neuron resolution. We are adapting the techniques of high-throughput next-generation DNA sequencing for the purposes of obtaining the structure of neuronal connectivity. We argue that because the cost of DNA sequencing has dropped precipitously over the last few years and the efficiency of these techniques is undergoing explosive growth, obtaining connectivity of sufficiently large networks is now feasible at sufficiently low cost. In our proposl, for example, we present preliminary data on the reconstruction of connectivity within a network of cultured mouse neurons containing about 1200 network nodes, which is the largest neuronal network reconstructed to date. To accomplish this task, we introduce unique short sequences of DNA into every neuron in the network. Because these short sequences uniquely label individual cells, we call them genetic barcodes. Using specifically designed viruses, we made these barcodes jump across synaptic junctions. Using enzymes called DNA recombinases, we connect barcodes from the host cell to the invader barcodes that travel across synapses into pairs. The barcode pairs carry information about network connectivity that can be obtained by DNA sequencing. Reconstructing neuronal connections from sequencing results presents unique computational and theoretical challenges that have never been dealt with before. In this project, we will build mathematical models that describe the underlying biological processes, test these models against experimental data, and use the resulting expertise to design accurate and efficient computational algorithms. Because of the need for feedback between theory, computational algorithms, and experiments, our project is intensely collaborative. The specific aims (SA) of this proposal include: SA 1: To develop a method of generating random barcodes in genomic DNA using the shufflon system. Here we will study, both theoretically and experimentally, the method of generating a large ensemble of barcode sequences using Rci recombinase that can shuffle DNA as a deck of cards. SA 2: To develop a biophysically realistic model for barcode processing within cells. In this SA we will study the mathematical models of barcodes jumping across synapses and their post-processing with the goal of identifying potential artifacts. The results of these models will be used for error correction in SA3. SA 3: To develop the computational pipeline for the reconstruction of connectivity from sequencing data. Here we will build a set of algorithms for efficient reconstruction of neuronal circuits from barcode pairs. Intellectual merit. The proposed research will contribute to biology on several levels. First, we will develop a novel set of technologies that will allow assaying neuronal connections with the single-neuron resolution. Second, we will build descriptive models for biophysics and combinatorics of DNA recombination that can be used in neuroscience and beyond. Finally, we will design a set of bioinformatics algorithms that are specific for the task o reconstructing neuronal connectivity. Broader impact. This project is based on the synergy between theoretical sciences, novel computational methods, and cutting-edge experiments in cellular neurobiology. The award will provide a unique cross-disciplinary environment for training of young neuroscientists. We expect that two postdoctoral fellows, specializing in theoretical and in experimental approaches, will receive training through this award. To broader society: Reconstructing neural circuits has significance for both fundamental studies of the brain and the studies of abnormalities of brain function. It is hard, if not impossible, to identify a medical condition involving the nervous system that would not affect neuronal connections.